| Mathematical difficulties (MD) often suffers defects with number concept, arithmetic, problem solving and other mathematical skills under the normal range of intelligence and suitable education environment. At present, many researchers want to explore the generation mechanism from perspective of physiology and cognitive psychology with mathematical difficulties children. There are three main points proposed from the perspective of cognitive psychology by scholars abroad:(1) The defective number module hypothesis proposes that a highly specific deficit of segment of the intraparietal sulcus (IPS) for number processing leads to difficulty in learning all kinds of number symbols with MD children; (2) The access deficit hypothesis states that mathematical difficulties originate from impairments in accessing numerical meaning from symbols rather than from difficulties in number processing; (3) The view of cognitive control ability defects considers that there is a close relationship between individual cognitive control ability (e.g., cognitive flexibility; cognitive monitoring; cognitive inhibition) and number processing. If MD children have defects in cognitive control, also can make them show the mathematical difficulties. Although the above three points have already been supported by experiments, the results are not consistent due to different subjects or all kinds of experimental materials and procedures probably.In recent years, Spatial-Number Association of Response Codes effect (SNARC) has caused widespread concern in the field of psychology. SNARC effect is a phenomenon that people will automatically connect numerosity and outer space in the number of processing:The small numbers (etc.1; 2) are connected to the left side of the space and the large numbers (etc.8; 9) are connected to the right side of the space. People show the faster reaction time on the left side of space for small numbers and the faster reaction time on the right side of space for large numbers. And for each number, the difference value between right side of the reaction time and left side of the reaction time can present a linear trend. This trend could show a decrease or a increase under different experimental conditions, and it also means that the SNARC effect will be weakened or enhanced with the change of the experimental conditions. At present, many researchers are exploring the characteristics and influences on the SNARC effect.In this study, MD children will be as experimental group and typical developing (TD) children will be as controlled. And it consults previous research paradigm to explore the characteristics of SNARC effect in different types of numerical information and cognitive controls using classical behavior experiments and modern eye movement technology. In order to further verify and provide experimental evidence about the defective number module, the access deficit hypothesis and the view of cognitive control ability defects, meanwhile this paper can provide some reference to diagnosis and educational rehabilitation of the children with mathematical difficulties.As a whole, this study is divided into two parts. The first part includes two studies, a total of four experiments. Two experiments of Study 1 were designed to explore the SNARC effect in the task with symbol numerical processing of MD children, and two experiments of Study 2 were designed to explore the SNARC effect in the task with nonsymbol number processing of MD children. The first part of the research hypothesis——If the defective number module hypothesis is established, MD children will show the defect in all types of (symbol and nonsymbol) number processing and the number of spatial representation. And MD children will not produce or produce smaller SNARC effect compared to children with TD; If the access deficit hypothesis is established, the SNARC effect will cause a difference between MD children and TD children only in number processing with symbol, and there is no difference in number processing with nonsymbol.The second part, namely Study 3 investigated the cognitive control (cognitive flexibility; cognitive monitoring; cognitive inhibition) of the children with MD through three experiments (Wisconsin Card Sorting Task & magnitude-colour switch task; parity-judgment task; directed forgetting task & position detecting task) to confirm whether the MD children have the defects of cognitive control. If they do, how the cognitive control impacts the SNARC effect. Under the premise of the defects of cognitive control with MD children, the second part of the research hypothesis are as follows:(1) The switch cost coming from magnitude-colour switch task will reduce the SNARC effect of TD children, but MD children will produce greater switch cost because of cognitive flexibility defects resulting the SNARC effect reduce more or even disappear; (2) TD children can use cognitive monitoring competence to adjustment attention control to adapt the conflict when performing the conflict processing and that leads to less SNARC effect in the conflict adaptation trials, but there is no corresponding change of MD children because of the defect ability of the cognitive monitoring; (3) When performing the position detecting task with the number as the distractor stimulus, MD children will produce a stronger SNARC effect due to the defect of cognitive inhibition compared to TD children. Surrounding the above problems, the main results of this study are as follows:Study 1 explored the MD children’s performance in the Arab symbol number processing. Experiment 1 was a magnitude comparison task in which the numerical information was worked as the target stimulus, and the results were that the efficiency of number processing with MD children was lower than TD children. There was no significant difference between MD children and TD children on the SNARC effect in horizontal direction, but MD children did not produce the SNARC effect in vertical direction like TD children. Experiment 2 was a position detecting task in which the numerical information was served as the distractor stimulus, and the results were that MD children did not show the defect of reaction time in the position detecting task, but MD children produced a stronger SNARC effect in horizontal direction compared to TD children. However, MD children also did not produce the SNARC effect in vertical direction like TD children, which suggested that MD children had the defect of connection direction in the number of spatial representation.Study 2 explored the MD children’s performance in the nonsymbol number processing. Experiment 3 was a magnitude comparison task in which the numerical information was as the target stimulus, and the results were that there was no difference between MD children and TD children in processing the small number range (1-4), but MD children took more time in processing the large number range (6-24) than TD children. Only TD children produced the SNARC effect in small number range and MD children did not produce the SNARC effect, which indicated MD children had the defect in the number of spatial representation and the defective number module hypothesis was verified; Experiment 4 was color discrimination task in which the numerical information was as the distractor stimulus, and the results were that MD children took more time in the color discrimination task than TD children. But liked experiment 2, MD children produced a stronger SNARC effect than TD children.Study 3 explored the MD children’s performance in cognitive control and the influence of individual cognitive control ability on the SNARC effect. Experiment 5 firstly showed MD children had the cognitive flexibility defects by Wisconsin Card Sorting Task, and MD children showed less categories completed (CC), but more preservative error (PE) and non-preservative error (NPE). In magnitude-colour switch task, although there was no difference on the error rate under the condition of task switching between TD children and MD children, the results of reaction time showed that MD children produced greater switch cost. The SNARC effect under the condition of task switching was less than the task repeating condition of TD children, but the SNARC effect disappeared under the condition of task switching because of more switching cost of MD children. Results showed that the worse of the individual cognitive flexibility, the smaller of the SNARC effect in the switching condition of the magnitude comparison task. Experiment 6 represented MD children had the defect of processing the parity in conflict processing of a parity-judgment and they did not produce the conflict adaptation effect as TD children. The SNARC effect vanished in the conflict adaptation trials of TD children, but the SNARC effect was no significant difference between conflict adaptation trials and conflict detection trials of the MD children. That illustrated MD children had the defect in the cognitive monitoring; Experiment 7 utilized directed forgetting task and eye tracking technique to indicate that when the numerical information was as the distractor stimulus, the cognitive inhibition could impact the SNARC effect. Directed forgetting task indicated that MD children’performance of recall scores under the clues to be forgotten (TBF) were lower than the TD children’and showed that the MD children had the defect in the cognitive inhibition. In addition, MD children produced a stronger SNARC effect than TD children when the numerical information was as the distractor stimulus appearing before the target stimulus, and the results showed that the less of individual cognitive inhibition, the stronger SNARC effect it would activate. In conclusion, this study considers that MD children hold a defective number module and a cognitive control ability defects.The value of this research and innovation points are:It investigated the characteristics in symbol and nonsymbol number processing through SNARC effect on MD children, and explored the MD children’ ability of cognitive control. It not only provides new evidence about the issues in numbering processing of MD children, but also affords certain reference to identify the core defect and education rehabilitation training of the MD children. Moreover, this research showed that the cognitive inhibition could impact the SNARC effect when performing the position detecting task with the number was served as the distractor stimulus appearing before the target stimulus, and it revealed the influence mechanism of the SNARC effect in further extent. |
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